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NEW YORK — President Bush’s proposed “guest-worker” program, which could grant amnesty to as many as 8 million illegal immigrants, has been pushed into the shadows at the Republican National Convention, much to the ire of conservatives.

The Bush-Cheney campaign said yesterday that downplaying the contentious issue, which split conservatives and moderates as the party drafted its platform in recent days, is strictly by design.

“You obviously need to focus on those issues that you think most voters care about,” campaign manager Ken Mehlman said, noting that the major issues are homeland security and the economy.

But some delegates are still quietly grumbling about the inclusion of the guest-worker plank in the platform.

“I don’t like it, and I don’t think it should be in there,” said one delegate from the Southwest who requested anonymity. “The program, as proposed by President Bush, does not represent conservative values and should have been done away with long ago.”

Still, the delegate, like several others, said the Republican Party has come together like never before and noted that after an often-testy debate on the issue while drafting the platform, the party is presenting a unified front.

Other delegates refused to say a cross word about the program, even anonymously. One delegate said despite strong misgivings about the guest-worker program, which he said is tantamount to “amnesty,” he would not publicly oppose the Republican platform or the president.

Wayne Johnson, a campaign consultant in Sacramento, Calif., a state with an illegal-alien problem, said it is not surprising that conservative delegates are providing the issue a pass — especially given the little effort that Mr. Bush has exerted to win approval for his program.

“There are too many other issues that are on the front burners; there’s only so many places you can spend political capital,” Mr. Johnson said. “This is not the year to spend that capital. Immigration is the kind of issue you deal with when you’re not dealing with election rhetoric.”

Under the proposed program, stalled in Congress, millions of illegal aliens who are using fake or stolen Social Security numbers would face no penalty and could remain in the country for an unspecified number of years, as long as they hold jobs that no Americans want.

Although the president said in January that the program would “provide incentives for temporary, foreign workers to return permanently to their home countries,” it has been criticized as amounting to a blanket amnesty because millions of illegal aliens would enjoy all employee rights, such as due process and Social Security benefits, given to those legally employed.

All of the estimated 8 million to 12 millions illegal immigrants already in the United States could apply for the right to work legally in the country for a three-year term that could be renewed repeatedly.

The Republican Party platform that was adopted this week strongly supported the president’s plan, causing a split between moderates and conservatives.

The party is walking a tightrope on the issue: It needs to hold onto or increase its take of minority voters — especially Hispanics — while not alienating its conservative base. Although the Bush-Cheney campaign is not pressing its guest-worker program, top officials have decided to sell the American Dream.

California Gov. Arnold Schwarzenegger, one of America’s most famous immigrants, said last night: “To my fellow immigrants listening tonight, I want you to know how welcome you are in this party. We Republicans admire your ambition. We encourage your dreams. We believe in your future.”

He said the United States gave him opportunities, and “I want other people to get the same chances I did, the same opportunities.”